Sketching the Derivative of a Function

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  • เผยแพร่เมื่อ 26 ส.ค. 2024
  • Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Buy my book!: '1001 Calculus Problems for Dummies' - you can get it on my website: patrickjmt.com/
    Sketching the Derivative of a Function - In this video, I sketch the derivative of two different functions. That is, I give the graph of y = f(x), and do a rough sketch of the graph f ' (x).
    For more free math videos, visit PatrickJMT.com

ความคิดเห็น • 510

  • @juliablanchard4994
    @juliablanchard4994 4 ปีที่แล้ว +626

    10 years later this man still saving us

  • @henryle4407
    @henryle4407 8 ปีที่แล้ว +680

    The moment when you realize that learning on youtube is more effective than learning from your actual teacher at school
    Thank you for saving my life!

    • @mikegarcia2279
      @mikegarcia2279 5 ปีที่แล้ว

      Agreed. Bless this video

    • @APSEAPSE
      @APSEAPSE 5 ปีที่แล้ว

      So true

    • @brymetheous2387
      @brymetheous2387 5 ปีที่แล้ว +2

      Yeah agreed, it's like my math professor just teaches me what to look up

  • @ST5S5
    @ST5S5 10 ปีที่แล้ว +179

    You taught this to me in 15 minutes better than my math teacher could in an hour. Thank you!

    • @sebon11
      @sebon11 5 ปีที่แล้ว +1

      Same here

    • @vpkasar7858
      @vpkasar7858 2 ปีที่แล้ว +2

      yall are old

  • @StephenRayner
    @StephenRayner 10 ปีที่แล้ว +80

    At around 5:38 I got slightly confused for a few seconds. To me you had your pen pointing down (i.e. negative) but you was saying it was getting more posative. But then I remembered we consider the direction from -x to x. so if the line is going from y = -5 to y = 5 from left ro right it is increasing and so is posative. If you consider the other way then you have negative but we consider from left to right.
    Hope this helps others who may have been slightly confused for a second.

  • @SuperKilltacular1
    @SuperKilltacular1 10 ปีที่แล้ว +301

    pretty sad when your instructor sucks at teaching and you have to come here just to learn how to graph a derivative...

  • @user-mk3yo6wo2h
    @user-mk3yo6wo2h 10 ปีที่แล้ว +30

    I want to point out in the first example, the graph is a cubic function. We can arbitrarily say x^3. Using some basic calculus rules, we can say the derivative of x^3 is 3x^2. 3x^2 is a parabola. That can help you identify which graph is the derivative. =)

  • @fyzy123
    @fyzy123 9 ปีที่แล้ว +82

    You are so much more helpful than my own professor. Can I pay you instead of her like seriously the class I'm taking is bullshit

    • @patrickjmt
      @patrickjmt  9 ปีที่แล้ว +29

      Works for me! Seriously though, sorry your class sucks!

    • @caseysheehan3182
      @caseysheehan3182 9 ปีที่แล้ว +7

      +patrickJMT But seriously you just helped my roommate and I with a quiz, TAKE MY MONEY

  • @trixiefortich3142
    @trixiefortich3142 5 ปีที่แล้ว +55

    "sorry for my bad graph" wait till you see my graphs....

  • @patrickjmt
    @patrickjmt  15 ปีที่แล้ว +32

    that is a nice turn-around grade-wise : )
    glad the vids helped

  • @Dean444ful
    @Dean444ful 8 ปีที่แล้ว +186

    Can you be my calculus teacher?

  • @whywasiborn851
    @whywasiborn851 21 วันที่ผ่านมา

    Your vid popped up on TH-cam for the first time in a few yrs and I just wanted to let you know you pulled me through HS and College.

  • @rahrahritaa
    @rahrahritaa 12 ปีที่แล้ว +24

    calc final in 2 hours! this is a great review

  • @PRDZ110
    @PRDZ110 3 หลายเดือนก่อน

    15 years later and ur still the goat man !

  • @memirandawong
    @memirandawong 10 ปีที่แล้ว +54

    Well, you have rendered my calculus book astonishingly useless with your videos! That's okay.
    The only thing I still need it for is the assigned HW problems!

  • @patrickjmt
    @patrickjmt  15 ปีที่แล้ว +6

    ya! that is probably possible! i will try to make one later today if i remember and dont get lazy! (gonna be a beautiful day today... dont wanna be inside making math videos!!) : )

  • @uriellopez6529
    @uriellopez6529 7 ปีที่แล้ว +2

    It's been years since I've been in school and I'm returning in a couple of weeks and your videos have made me confident in my math skills once more!!! Thank you so much!!!

  • @SammyWinFL
    @SammyWinFL 13 ปีที่แล้ว +1

    @patrickJMT A great teacher like yourself will surely be repaid for their good deeds as a person in one way or another! I'm studying for the PCAT exam and this helped so much.
    Thank you Patrick

  • @rotate58
    @rotate58 14 ปีที่แล้ว +1

    I can't thank you enough, your fantastic explanation and teaching method helped me to understand what close to three hours of confusing instruction with my own teacher could not. Thank you!

  • @Boombocks_Studio
    @Boombocks_Studio 3 ปีที่แล้ว +1

    Over 11 years since you uploaded this video, but thank you for it. My professor is FUCKING DOGSHIT and not teaching us, instead relying on the eText and short "lecture" videos from the code for our required materials. It's pathetic but I'm learning more from your content than anything in this $200 book code material.

  • @ilikedetectives
    @ilikedetectives 14 ปีที่แล้ว +3

    Thank you so much!!! My teacher skipped in class this part and now I'm having trouble with doing the hw. You just saved my life!!!!

  • @dannyzuko1850
    @dannyzuko1850 11 ปีที่แล้ว +1

    This probably won't mean a lot with the countless 'thank you's you receive everyday, but I seriously want to thank you. This is EXTREMELY helpful. Bless YOU!

  • @TheWarfare07
    @TheWarfare07 7 ปีที่แล้ว +4

    this is great. i learned so much more in 15 mins than being in class for 2 damn hours. thanks

  • @mirandashirley4697
    @mirandashirley4697 11 ปีที่แล้ว +3

    Thank you so much! My teacher flies through our calc lessons so this helps TONS. I really appreciate it.

  • @DeJayHank
    @DeJayHank 15 ปีที่แล้ว +1

    failed my first exam. 2 months later i had another chance. used your tutorials for 2 days and got top grade.
    thanks alot mate =)

  • @Countrycon
    @Countrycon 13 ปีที่แล้ว +1

    You are hands down better than any math teacher I've ever had.

  • @kingsley182
    @kingsley182 13 ปีที่แล้ว

    Desperate attempts have led me to the internet. I found your video. THANK GOD. I AM GOING TO ACE THIS DERIVATIVE GRAPH IN MY MATHEMATICS EXAMINATION TOMORROW. THANK YOU.

  • @hartake6667
    @hartake6667 9 ปีที่แล้ว +9

    Boss! With just the first 5 minutes I've been able to make deductions to answer 5 questions on the assignment correctly.

  • @puckSHOCK
    @puckSHOCK 14 ปีที่แล้ว +1

    I started Calculus a month ago, in that time, I think I've watched a majority of your calculus videos.
    Thank you for saving me :)

  • @patrickjmt
    @patrickjmt  13 ปีที่แล้ว

    @MrAznSoldier thanks for taking time to watch my videos : )

  • @shahadmerani3116
    @shahadmerani3116 ปีที่แล้ว

    the graph I’ve been struggling with for 3 days..u basically saved my life lol 💀

  • @PossumPog64
    @PossumPog64 ปีที่แล้ว

    2023 and this man is still saving the lives of all STEM majors

  • @1MrShiny
    @1MrShiny 10 ปีที่แล้ว

    you taught me in 10 minutes, what my textbook couldn't teach me in 2 weeks. You are a miracle, i suddenly feel more confident about my upcoming test.
    Thanks!

  • @helioselenus
    @helioselenus 13 ปีที่แล้ว

    Awesome. Maybe the title should be "Finding the derivative of a function graphically." It took me awhile to find the right video. Thanks.

  • @joshuahurtado882
    @joshuahurtado882 5 ปีที่แล้ว +5

    dude, well done.
    I finally understand this concept, my instructor tweakinggggggg.

  • @safar127
    @safar127 12 ปีที่แล้ว +1

    I WAS SO LOST BUT U MADE ME FIND MY WAY AGAIN THANKS!!!

  • @mintbreakart
    @mintbreakart 11 ปีที่แล้ว +1

    THANK YOU SO MUCH! This is the only bit I didn't understand. And I got it immediately.

  • @patrickjmt
    @patrickjmt  12 ปีที่แล้ว +1

    @PSliveNlove happy to help!

  • @patrickjmt
    @patrickjmt  15 ปีที่แล้ว

    thats true... if i called it the 'step function' i spoke incorrectly! it does clearly 'jump around' though

  • @Marina-zn8ip
    @Marina-zn8ip 9 ปีที่แล้ว +1

    This was so helpful!! Have a calculus exam next hour and this video has been way more productive than anything my teacher ever said.

  • @madelyndriver1213
    @madelyndriver1213 10 ปีที่แล้ว +2

    Thanks for the lesson. I got a high fever the second week of classes and am trying to teach myself Calc before classes start again on Tuesday. This helped a bunch!

  • @xxpunkxxgirl
    @xxpunkxxgirl 12 ปีที่แล้ว +1

    Awesome!! We're doing this in calc now, and you taught me better in 15 mins than my teacher did in a whole week.

  • @lizzyjane1361
    @lizzyjane1361 10 ปีที่แล้ว +2

    THANK YOU! 6 days before my mocks and I was freaking out about this. You're my hero :)

  • @valkyrie034
    @valkyrie034 13 ปีที่แล้ว +1

    Thanks for the help, keep the videos rolling. First semester Calculus, and was having trouble with graphing them- couldn't wrap my brain around it, but I've got it now!

  • @mattreese
    @mattreese 14 ปีที่แล้ว +1

    I've watched many of your videos, they are a huge help. Thanks for breaking it down into lemans terms for me.

  • @patrickjmt
    @patrickjmt  12 ปีที่แล้ว

    @Xx0Mystic0xX i will also post it as a video response in the comment section

  • @mf7114
    @mf7114 12 ปีที่แล้ว +1

    Thank you so much! I am in calc my freshman year of college and even though I go into office hours and such, I had NO idea what was going on. Thanks for explaining it in plain english and not some fancy math lingo :). You're awesome!

  • @MoonMoon-bj9jr
    @MoonMoon-bj9jr 3 ปีที่แล้ว

    this man still coming clutch after 11 years

  • @elyazzoo
    @elyazzoo 12 ปีที่แล้ว +1

    hey i really appreciate this my teacher doesn't really fit my learning style at all so you are literally getting me through calculus

  • @vishalmishra9214
    @vishalmishra9214 2 หลายเดือนก่อน

    after 15 years still you are best in this domain.🤗

  • @carmelamorano6296
    @carmelamorano6296 3 ปีที่แล้ว

    It’s 2020 and this is still helping people

  • @keithbt430888
    @keithbt430888 13 ปีที่แล้ว

    this makes graphing derivatives seem too easy, i hope the school you teach at really appreciates you. :)

  • @patrickjmt
    @patrickjmt  14 ปีที่แล้ว

    @rosepetals1002 u r very welcome

  • @sportster832
    @sportster832 9 ปีที่แล้ว

    You have done what my math teacher could not do

  • @EmilyDeibert
    @EmilyDeibert 13 ปีที่แล้ว +1

    You probably just saved my life for my calc test tomorrow! Keep up the good work!

  • @VinUnleaded182
    @VinUnleaded182 13 ปีที่แล้ว +1

    thank you so much. spent hours to wrap my head around this and your video cleared this up a lot

  • @Beauty_by_Summer
    @Beauty_by_Summer 11 ปีที่แล้ว

    omg sir u dont know how much youve helped me! im a senior in high school and im taking AP calc, the teacher never explains stuff! but u made it much more clear. thank u!

  • @colinwhitlock5148
    @colinwhitlock5148 4 ปีที่แล้ว +3

    I'm just confused as to how we figure out the minimum y value of f'(x) when we aren't actually given any values on the graph

  • @juliankashama1279
    @juliankashama1279 4 ปีที่แล้ว

    Hey Patrick! Thank you for helping me with my engineering degree. I feel like I know You! We spent long math nights together. 🤣🤣Graduated last year. Just want to saying thank you. You have a God given gift! You helped me out big time!! Thank you.
    Writing from Botswana! Much love!

    • @patrickjmt
      @patrickjmt  4 ปีที่แล้ว +1

      Happy to help!

  • @macallancruff2828
    @macallancruff2828 10 ปีที่แล้ว

    I have a crazy math teacher who looked at me like I was crazy when I asked her what the heck she was doing. Thank you so much for clarifying! Keep being awesome!

  • @ceemihail
    @ceemihail 6 ปีที่แล้ว +1

    I've been having one of those day for 3 weeks now trying to get calculus, thx for the videos.

  • @rzehrahayder7788
    @rzehrahayder7788 5 ปีที่แล้ว +2

    honestly thank you, seriously needed this

  • @patrickjmt
    @patrickjmt  12 ปีที่แล้ว +4

    glad i could help you out :)

  • @0bsessionist
    @0bsessionist 13 ปีที่แล้ว +1

    You're better than my calculus professor! Thank you so much!! You're saving my grade!

  • @MrCaRTom
    @MrCaRTom 14 ปีที่แล้ว +1

    i have a math test today in a few hours, been watching your videos for the stuff i had trouble with and since i went over them so much, that's the stuff i feel better about :) i hope i do good on the test..

    • @LilbabyonYT
      @LilbabyonYT ปีที่แล้ว

      I hope you aced that test. How’s life?

  • @rinarox912
    @rinarox912 11 ปีที่แล้ว

    i just realized you're left handed!!!same here! you're good at not smudging over what you write!!! I always end up smudging whatever I write on the board because my hand just goes over it haha
    and thank you for the video! it's very helpful

  • @sakaklovas
    @sakaklovas 14 ปีที่แล้ว

    Um... you just taught me in 15 minutes what I was struggling to learn for days...thank you.

  • @omarmartinez399
    @omarmartinez399 10 ปีที่แล้ว +1

    dude, you explain this with such great clarity thank you!

  • @syn586
    @syn586 7 ปีที่แล้ว +11

    You were really helpful man.
    Really.Thankyou.
    And no your sketching isn't that bad.

  • @oris314
    @oris314 13 ปีที่แล้ว

    Thanks bunch! i have calculus homework on graphing derivatives with only having the graph of f(x) and didn't understand it at all. now i can actually get my homework done!

  • @patrickjmt
    @patrickjmt  12 ปีที่แล้ว

    because the slopes of the tangent lines are constant over those intervals

  • @lizbizwiz1238
    @lizbizwiz1238 6 ปีที่แล้ว

    Dude, I have a Derivative test tomorrow and you are a lifesaver!

  • @rowshawn0068
    @rowshawn0068 4 ปีที่แล้ว

    11 years later and still saving my butt

  • @scribbledheartz
    @scribbledheartz 12 ปีที่แล้ว

    This made a hug impact on my graphing ability. In my calc book there's questions but no explanation on how to go about graphing derivatives of a function. So thank you!! :)

  • @turbocharged06
    @turbocharged06 14 ปีที่แล้ว

    thank you! my book didn't cover this and you know how calculus professors are...

  • @Qasso124
    @Qasso124 6 ปีที่แล้ว +4

    almost 10 years, I come here yearly to make sure I remember how to sketch the derivative of graphs :|

  • @DannyLinux
    @DannyLinux 12 ปีที่แล้ว

    @bwill115 its because the tangent line is pointing towards the positive Y coordinate as it goes from -infinity to +infinity! (:

  • @patrickjmt
    @patrickjmt  13 ปีที่แล้ว

    @Ilikeroots ops, thanks for posting this, sorry it took e 3 months to notice. it is gone now : )

  • @SnoopPwn09
    @SnoopPwn09 11 ปีที่แล้ว

    Here is something that helps me... start with the orignal function (f). If you see that it is increasing then the f'(x) is positive. If the original function (f) in decreasing then f'(x) is negative. Then you can repeat this for f''(x). If f'(x) is increasing, then f''(x) is positive or concave up. If f'(x) is decreasing, then f''(x) is negative or concave down. In addition, if you are looking for extemas use f'(x) and if you solving for points of inflection, use f''(x).

  • @Ericka5651
    @Ericka5651 12 ปีที่แล้ว

    this video seriously just saved me from making a big mistake on my calc exam tomorrrow. Why does this always seem so easy when someone else is graphing this lol

  • @patrickjmt
    @patrickjmt  12 ปีที่แล้ว +2

    glad i could help you :)

  • @rachelmgosse2195
    @rachelmgosse2195 4 ปีที่แล้ว

    oml a king thank you. you helped me understand and now it all clicks!!!

  • @obikiller1
    @obikiller1 12 ปีที่แล้ว

    Thanks so much freshman high school day before test explains a lot.

  • @patrickjmt
    @patrickjmt  14 ปีที่แล้ว

    @rotate58 glad i was able to help make some sense of it. perhaps your instructor helped 'warm you up ' though : )

  • @TheTastyAsian
    @TheTastyAsian 11 ปีที่แล้ว +1

    Omg you're such an amazing teacher!!! I've had at least 5 different ppl try to teach me and I still didn't get it--but YOU ACTUALLY MAKE SENSE AND THE CONCEPT IS SO CLEAR NOW! Thank you so much!

  • @OverlyCuriousEngineer
    @OverlyCuriousEngineer 11 ปีที่แล้ว

    You sir, are the best tutuor to ever step on the face of the earth. Hats off!

  • @CL-lr9wh
    @CL-lr9wh 9 ปีที่แล้ว

    I spent three semester on calculus and didn't know how to sketch this. And you helped me just in a few minutes. Thanks!!!

  • @vivian164
    @vivian164 8 ปีที่แล้ว +15

    OMFG THANK YOU

  • @patrickjmt
    @patrickjmt  13 ปีที่แล้ว

    @agentlopez1 used to teach, but with 'only' a masters, you can not find full time university positions. only short contracts with poor pay and no insurance or benefits. so, i no longer teach, except on youtube!

  • @shannonsullivan3193
    @shannonsullivan3193 11 ปีที่แล้ว +1

    So unbelievably helpful! Thank you so much!

  • @animemewmew7
    @animemewmew7 9 ปีที่แล้ว +2

    Thank you Patrick :) You are helping me to understand and relearn (better, this time) calculus before my AP exam next Tuesday.

    • @mblackops2
      @mblackops2 6 ปีที่แล้ว

      catsithkellas I'm taking AP Calc rn. I'm thinking about dropping out. Is it worth it? School has started for like a month now and I have a D in the class. I got an F on my quiz and on my test.

  • @LeonardNdegwazugzwang
    @LeonardNdegwazugzwang 11 ปีที่แล้ว

    You have THE best vids in calculus THANKS

  • @andehz
    @andehz 12 ปีที่แล้ว

    You're graph is 99.9% better than any teacher/professor out there. Quit crying.
    With that said, you own nerd.
    Respect

  • @coyotes2012
    @coyotes2012 12 ปีที่แล้ว

    Your videos always give me a good refresh for my college calculus class. Thank you VERY much for these videos. Helpful and to the point

  • @Pika163
    @Pika163 14 ปีที่แล้ว

    OH MY GOODNESS this was HEAVEN SENT!

  • @horsesofcourses1
    @horsesofcourses1 10 ปีที่แล้ว +6

    This actually, logically, makes sense. I UNDERSTAND NOW!!!!!!!

  • @sunlitmoss
    @sunlitmoss 10 หลายเดือนก่อน

    this was so helpful you just saved my ap calc grade

  • @eatyoriceful
    @eatyoriceful 12 ปีที่แล้ว

    AMAZING video thank you soooo much
    i was about to give up on this curve sketching crap TT-TT but this video explains it very clearly

  • @adamdebesai
    @adamdebesai 11 ปีที่แล้ว

    With your explanation and teaching, who wouldn't get this? Great video!!!

  • @EGabrielFulton
    @EGabrielFulton 11 ปีที่แล้ว

    You my friend, deserve a medal.

  • @CHANNEL_MOUKTAR
    @CHANNEL_MOUKTAR 13 ปีที่แล้ว

    thank you for you video I had a hard time getting the derivative of the graph of f(x).